The Analyticity for the Product of Analytic Functions on Octonions and Its Applications

Given two left Oc-analytic functions f, g in some open set Ω of R8, we obtain some sufficient conditions for fg is also left Oc-analytic in Ω. Moreover, we prove?fλ that is a left Oc-analytic function for any constants λ∈Oc if and only if is a complex Stein-Weiss conjugate harmonic system. Some applications and connections with Cauchy-Kowalewski product are also considered.

Multi-objective Day-ahead Polarity Switching Optimization for Voltage Unbalance in Bipolar DC Distribution Networks

Bipolar direct current(DC)distribution networks can effectively improve the connection flexibility for renewable generations and loads.In practice,concerns regarding the potential voltage unbalance issue of the distribution networks and the frequency of switching still remain.This paper proposes a day-ahead polarity switching strategy to reduce voltage unbalance by optimally switching the polarity of renewable generations and loads while minimizing the switching times simultaneously in the range of a full day.First,a multi-objective optimization model is constructed to minimize the weighted sum of voltage unbalance factors and the sum of number of switching actions in the day based on the power flow model.Second,a two-step solution strategy is proposed to solve the optimization model.Finally,the proposed strategy is validated using 11-node and 34-node distribution networks as case studies,and a switching and stabilizing device is designed to enable unified switching of renewable generations and loads.Numerical results demonstrate that the proposed strategy can effectively reduce the switching times without affecting the improvement of voltage balance.

Coordination Control of Power Flow Controller and Hybrid DC Circuit Breaker in MVDC Distribution Networks

The two main challenges of medium voltage direct current(MVDC)distribution network are the flexible control of power flow(PF)and fault protection.In this paper,the power flow controller(PFC)is introduced to regulate the PF and inhibit the fault current during the DC fault.The coordination strategy of series-parallel PFC(SP-PFC)and hybrid DC circuit breaker(DCCB)is proposed.By regulating the polarity and magnitude of SP-PFC output voltage during the fault,the rising speed of fault current can be suppressed so as to reduce the breaking current of hybrid DCCB.The access mode of SP-PFC to the MVDC distribution network and its topology are analyzed,and the coordination strategy between SP-PFC and hybrid DCCB is investigated.Moreover,the emergency control and bypass control strategies of SP-PFC are developed.On this basis,the mathematical model of SP-PFC in different fault stages is derived.With the equivalent model of SP-PFC,the fault current of the MVDC distribution network can be calculated accurately.A simulation model of the MVDC distribution network containing SP-PFC is established in MATLAB/Simulink.The fault current calculation result is compared with the simulation result,and the effectiveness of the proposed coordination strategy is verified.